His name meant Last king, and he was named so because of a prophesy by Malbeth the Seer:'

"Arvedui you shall call him, for he will be the last in Arthedain. Though a choice will come to the Dúnedain, and if they take the one that seems less hopeful, then your son will change his name and become king of a great realm. If not, then much sorrow and many lives of men shall pass, until the Dúnedain arise and are united again." — Appendix A: "Gondor and the Heirs of Anárion"